Preface: If a bar magnet is cut in half, we are left with say N-S--cut--N-S allinged along the z axis. Then the S and N ends are attracted to each other. This attraction is due to the "fringing" or non-uniform B field of the poles. That is the component of the B field that is normal to the "circular" magnetizing currents creates a Lorentz force along the Z axis. So as the S side moves closer to N (the gap is reduced) the normal component of the B field increases. Finally My questions: (1) Why does the magnitude of the normal component increase. Is it because the magnitude of dB/dz is larger as the gap is closed? Or because the overall magnitude of B is larger and therefore it normal component is correspoundly larger? or ? (2) When the Magnets touch, no air gap at all, shouldn't the force go to zero since the fringing or db/dz would go to zero or be greatly reduced? But I don't think this happens because my magnets stick to my Fridge....Help!